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By R. Erickson

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Line-commutated rectifiers 18. Pulse-width modulated rectifiers Fundamentals of Power Electronics 33 Chapter 1: Introduction Part V. 8 2 F = fs / f0 Fundamentals of Power Electronics 34 Chapter 1: Introduction Part V. Resonant converters 19. 20. 7 nF Epwm 50 kHz v – 7 VM = 4 V R R2 L = 50 µΗ fs = 100 kΗz –40 dB R1 11 kΩ 4 Xswitch R=3Ω + C 3 4 0 dB iLOAD 3 500 µF + – A. B. C. D. 1. 2. 3. 4. 5. 6. 2. Inductor volt-second balance, capacitor charge balance, and the small ripple approximation Actual output voltage waveform, buck converter iL(t) 1 Buck converter containing practical low-pass filter L + vL(t) – Vg + iC(t) 2 + – C R v(t) – Actual output voltage waveform Actual waveform v(t) = V + vripple(t) v(t) V v(t) = V + vripple(t) dc component V 0 t Fundamentals of Power Electronics 7 Chapter 2: Principles of steady-state converter analysis The small ripple approximation Actual waveform v(t) = V + vripple(t) v(t) v(t) = V + vripple(t) V dc component V 0 t In a well-designed converter, the output voltage ripple is small.

Basic magnetics theory 14. Inductor design 15. Transformer design Fundamentals of Power Electronics 31 Chapter 1: Introduction Part IV. Modern rectifiers, and power system harmonics Pollution of power system by rectifier current harmonics A low-harmonic rectifier system boost converter i(t) ig(t) + iac(t) vac(t) L vg(t) Q1 – vcontrol(t) vg(t) multiplier X + D1 C v(t) R – ig(t) Rs PWM va(t) v (t) +– err Gc(s) vref(t) = kx vg(t) vcontrol(t) compensator controller Harmonic amplitude, percent of fundamental 100% 100% 91% 80% THD = 136% Distortion factor = 59% 73% 60% iac(t) + 52% 40% 32% 19% 15% 15% 13% 9% 20% 0% 1 3 5 7 Ideal rectifier (LFR) 9 11 13 15 17 19 Model of the ideal rectifier vac(t) 2 p(t) = vac / Re Re(vcontrol) + v(t) – – ac input Harmonic number i(t) dc output vcontrol Fundamentals of Power Electronics 32 Chapter 1: Introduction Part IV.

Fundamentals of Power Electronics 15 Chapter 2: Principles of steady-state converter analysis Inductor volt-second balance: Buck converter example vL(t) Vg – V Inductor voltage waveform, previously derived: Total area λ t DTs –V Integral of voltage waveform is area of rectangles: Ts λ= vL(t) dt = (Vg – V)(DTs) + ( – V)(D'Ts) 0 Average voltage is vL = λ = D(Vg – V) + D'( – V) Ts Equate to zero and solve for V: 0 = DVg – (D + D')V = DVg – V Fundamentals of Power Electronics 16 ⇒ V = DVg Chapter 2: Principles of steady-state converter analysis The principle of capacitor charge balance: Derivation Capacitor defining relation: dv (t) iC(t) = C C dt Integrate over one complete switching period: vC(Ts) – vC(0) = 1 C Ts iC(t) dt 0 In periodic steady state, the net change in capacitor voltage is zero: 0= 1 Ts Ts iC(t) dt = iC 0 Hence, the total area (or charge) under the capacitor current waveform is zero whenever the converter operates in steady state.